THEORY OF POLYCONIC PROJECTIONS. 31 



or, on passing to exponentials, 



e'=taag+|) 



." + .-'= tan (|+|)+cotg + 



(M)-^-<f-^f) 



«n(| + |)cos(|+|) 



sm^ 



2smg + |)cosQ+|) sin(| + v>) 



cos (p 



or 



2 — =s^^ ^ 



cosh (7 = sec ^ 



-=i = sinn a 



sinh (J = Vcosh^ cr — 1 



sinh cr = -y/sec^ (^ — 1 = tan (j^?. 



sinh %\ = i sin'X. 



cosh iX = cos X. 

 If we take 



we obtain the stereographic meridian projection. 



